Simplify the following expression: $y = \dfrac{6z^2 - 30z + 24}{z - 4} $
Explanation: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $6$ , so we can rewrite the expression: $ y =\dfrac{6(z^2 - 5z + 4)}{z - 4} $ Then we factor the remaining polynomial: $z^2 {-5}z + {4} $ ${-4} {-1} = {-5}$ ${-4} \times {-1} = {4}$ $ (z {-4}) (z {-1}) $ This gives us a factored expression: $\dfrac{6(z {-4}) (z {-1})}{z - 4}$ We can divide the numerator and denominator by $(z + 4)$ on condition that $z \neq 4$ Therefore $y = 6(z - 1); z \neq 4$